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The Weekly Warlock Wind-Up: Cups (answer)

March 12, 2010 — Veliaf

Let’s say a factory recycles paper cups. In this factory, seven used cups are needed for each new cup. From 721 used cups, how many new cups can possibly be made in total?

A short question which seems to have a very complex answer, considering the amount of different solutions people came up with! The truth awaits beyond the break, although I can assure you that the above diagram was used neither to make the puzzle seem more complex, nor to give you hints. I just liked it.

The trick here is remembering that, after you make some cups, you can use the newly-created ones to make even more, and so on.

So the first step is pretty simple: take the original amount, 721, and divide by 7. Handily, it divides perfectly, giving us 103. Now we need to keep going!

Next, we divide 103 by 7. This gives us 14 whole cups (now a total of 103 + 14 = 117 new cups) and leaves us with a remainder of 5 left over.

Then we can divide that 14 by 7 to gives us 2 (now a total of 117 + 2 = 119 new cups).

These last 2, together with the 5 which were left over before, gives us 7 cups left and of course we can use these to make 1 more cup.

Finally we can add this 1 to our total, bringing the final amount to 119 + 1 = 120 cups!